In a tree 3/5 of the birds are robins while the rest are bluejays. If 1/4 of the robins are female and 3/4 of the bluejays are female, what fraction of the birds in the tree are male?
A. 7/15 B. 1/2 C. 11/20 D. 2/3 E. 7/10
(C) First we need to determine the fraction of the birds that are bluejays: (fraction that are bluejays) = 1 (total birds) – 3/5 (fraction that are robins) = 5/5 (total birds) – 3/5 (fraction that are robins) = 2/5 Next, determine the fraction of all the birds that are female: (fraction of all birds that are female) = (3/5) × (1/4) (female robins) + (2/5) × (3/4) (female bluejays) = 3/20 (female robins) + 6/20 (female bluejays) = 9/20 of all birds are female. The fraction of male birds then is: (fraction of all birds that are male) = 1 (total birds) – 9/20 (female birds) = 20/20 (total birds) – 9/20 (female birds) = 11/20 of all birds are male.
The alternative way: Suppose there were 100 birds in the tree. Using the fractions in the question, you can fill up this table.
Therefore 55 out of 100 birds are male, implying a fraction of 55/100 = 11/20.
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